The model of a rigid heat conductor with memory is considered. Specifically, in the one-dimensional case, a connection, via Cole-Hopf Transformation, between the linear integro-differential evolution equation which describes heat conduction with memory and a nonlinear partial integro-differential equation of hyperbolic type is established. Notably, when the heat conductor is homogeneous, as well as when the homogeneity hypothesis is removed, the differential operator of the transformed nonlinear partial differential equation is of hyperbolic type.
Nonlinear Hyperbolic Equations and Linear Heat Conduction with Memory / Carillo, Sandra. - STAMPA. - 50(2010), pp. 63-70. ((Intervento presentato al convegno 11th EUROMECH-MECAMAT Conference on Mechanics of Microstructured Solids - Cellular Materials, Fibre Reinforced Solids and Soft Tissues tenutosi a Torino, ITALY nel MAR 10-14, 2008. - LECTURE NOTES IN APPLIED AND COMPUTATIONAL MECHANICS. [10.1007/978-3-642-05171-5_7].
Nonlinear Hyperbolic Equations and Linear Heat Conduction with Memory
CARILLO, Sandra
2010
Abstract
The model of a rigid heat conductor with memory is considered. Specifically, in the one-dimensional case, a connection, via Cole-Hopf Transformation, between the linear integro-differential evolution equation which describes heat conduction with memory and a nonlinear partial integro-differential equation of hyperbolic type is established. Notably, when the heat conductor is homogeneous, as well as when the homogeneity hypothesis is removed, the differential operator of the transformed nonlinear partial differential equation is of hyperbolic type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
